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Posted by **pat** on Saturday, December 4, 2010 at 1:37am.

4x^2 + 16y^2 - 64x - 32y + 208 = 0

- Precalc -
**Henry**, Sunday, December 5, 2010 at 9:05pm4X^2 + 16Y^2 - 64X - 32Y + 208 = 0.

Rearrange variables:

4X^2 - 64X + 16Y^2 - 32Y = -208,

Divide both sides by 4:

X^2 - 16X + 4Y^2 - 8Y = -52,

Complete the square:

X^2 - 16X + (-16/2)^2 + 4(Y^2 - 2Y +

(-2/2)^2) = -52 + 64 + 4 = 16,

Simplify:

X^2 - 16X + 64 + 4(Y^2 - 2Y + 1) = 16.

Write the perfect squares as binomials:

(X - 8)^2 + 4(Y - 1)^2 = 16,

Divide both sides by 16 and get:

(X - 8)^2 / 16 + (Y - 1)^2 / 4 = 1.

C(h , k) = C(8 , 1).

a^2 = 16,

a = +- 4.

b^2 = 4,

b = +-2.

Major Axis:

V1(X1 , Y1), C(8 , 1), V2(X2 , Y2).

h - X1 = a,

X1 = h - a,

X1 = 8 - 4 = 4.

Y1 = Y2 = K = 1.

X2 - h = a,

X2 = h + a,

X2 = 8 + 4 = 12.

Minor Axis:

V4(X4 , Y4)

C(8 , 1)

V3(X3 , Y3)

X3 = X4 = h = 8.

k - Y3 = b,

Y3 = k - b,

Y3 = 1 - 4 = -3.

Y4 - k = b,

Y4 = k + b,

Y4 = 1 + 4 = 5.

Center and Vertices:

C(8 , 1)

V1(4 , 1)

V2(12 , 1)

V3(8 , -3)

V4(8 , 5).

Complete the square:

- Precalc -
**Henry**, Sunday, December 5, 2010 at 9:25pmCORRECTION:

b = 2,

Y3 = k - b,

Y3 = 1 - 2 = -1.

Y4 = k + b,

Y4 = 1 + 2 = 3.

V3(8 , -1)

V4(8 , 3).

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